Atmos. Chem. Phys., 2, 93–98, 2002
www.atmos-chem-phys.org/acp/2/93/
Atmospheric
Chemistry
and Physics
NAT-rock formation by mother clouds: a microphysical model study
S. Fueglistaler1 , B. P. Luo1 , C. Voigt1 , K. S. Carslaw2 , and Th. Peter1
1 Atmospheric
2 School
and Climate Science, ETH Zürich, Switzerland
of the Environment, University of Leeds, Leeds, UK
Received: 11 December 2001 – Published in Atmos. Chem. Phys. Discuss.: 14 January 2002
Revised: 19 April 2002 – Accepted: 29 April 2002 – Published: 15 May 2002
Abstract. Polar stratospheric clouds (PSCs) of type 1a or 1aenh containing high number densities of nitric acid trihydrate
(NAT) particles, can act as mother clouds for extremely large
NAT particles, termed NAT-rocks, provided the air below the
clouds is supersaturated with respect to NAT. Individual NAT
particles at the cloud base fall into undepleted gas phase and
rapidly accelerate due to a positive feedback between their
growth and sedimentation. The resulting reduction in number density is further enhanced by the strong HNO3 depletion within a thin layer below the mother cloud, which delays subsequent particles. This paper introduces the basic
microphysical principles behind this mother cloud/NAT-rock
mechanism, which produces 10−4 cm−3 NAT-rocks with
radii around 10 µm some kilometers below the mother cloud.
The mechanism does not require selective nucleation and
works even for a monodisperse particle size distribution in
the mother cloud.
1 Introduction
Denitrification of the Arctic stratospheric vortex is believed to enhance halogen-catalyzed chemical reactions leading to ozone depletion (WMO, 1999; Waibel et al., 1999;
Tabazadeh et al., 2001; Gao et al., 2001). A major finding of
the SOLVE/THESEO-2000 campaign is the widespread occurrence of large nitric acid hydrate particles of up to 10 µm
in radius in extremly low number densities (n ≈ 10−4 cm−3 )
(Fahey et al., 2001). Most likely these large particles
were composed of NAT ≡ HNO3 · 3 H2 O (commonly called
“NAT-rocks” [Fahey, pers. comm.]). They are mostly out
of thermodynamic equilibrium with the ambient gas phase
due to their low number densities, which leads to long particle/gas phase equilibration times. In turn, this allows the
Correspondence to: S. Fueglistaler
([email protected])
c European Geophysical Society 2002
particles to grow to the observed sizes which enable them to
sediment rapidly and thus to efficiently denitrify the corresponding layers of the polar stratosphere.
PSCs of type 1a and 1a-enh, presumably consisting of
NAT, have been extensively studied for several years (Browell et al., 1990; Toon et al., 1990; Tsias et al., 1999; Toon
et al., 2000; Voigt et al., 2000). While 1a-enh PSCs have
typical number densities n ≈ 0.1 cm−3 and are therefore
close to thermodynamic equilibrium with the ambient gas
phase, type 1a PSCs have lower particle number densities
>
and longer equilibration times ( ∼
1 day) (Biele et al., 2001).
>
−2
−3
NAT clouds with n ∼ 10 cm have limited particle radii
<
r∼
2.5 µm. Such particles have only small sedimentation velocities and thus cannot lead to efficient denitrification. Here we show that dense NAT clouds can be efficient
sources for NAT-rocks (a similar mechanism is suggested by,
Dhaniyala et al., 2002) explaining their observed characteristics with respect to particle number density and size without highly selective nucleation, e.g. homogeneous freezing
of NAT (Tabazadeh et al., 2001).
2
The basic mechanism
In this study a mechanism is proposed where NAT clouds
>
with high particle number densities (n ∼
0.01 cm−3 ) act as
“mother clouds”, that is, as efficient sources for NAT-rocks
via sedimentation. Mother clouds are close to thermodynamic equilibrium, i.e. the saturation ratio SNAT of HNO3
with respect to NAT within the cloud is close to unity. However, below the cloud where NAT particles are absent or extremly low in number density, SNAT may be larger than 1 (see
e.g. Fueglistaler et al., 2002, for observations). NAT particles
that sediment out of the mother cloud fall into this supersaturated air, begin to grow and hence accelerate. In this paper
we show results of a model that solves the coupled equations
for particle growth, sedimentation and gas phase depletion.
94
Fueglistaler et al.: NAT-rock formation by mother clouds
Altitude
(a) S<1, n=0
S=1,n>10
(b) S<1, n=0
- 2
S=1,n>10
S~1
S>1,n~10
- 2
4
S>1, n=0
S>1, n=0
S<1, n=0
S<1, n=0
Mother
cloud
FRL
SNAT < 1
Flux ~
const.
Fig. 1. Schematic vertical cross section of NAT particle sedimentation out of a mother cloud floating in supersaturated air. S is the
saturation ratio with respect to NAT, n the NAT particle number
density. (a) A few hours after mother cloud formed. (b) A few days
later after NAT particles have sedimented out. The flux reduction
layer (FRL) is shown schematically. Sizes in drawing not in proportion, deformation in (b) sketches deformation caused by wind
shear.
However, we will first present a theoretical discussion to gain
insight into the suggested mechanism.
To break down the complex interplay of particle growth,
acceleration and gas phase depletion, we first consider the
hypothetical case where the growing particles do not deplete the gas phase. All particles then experience the same
growth and sedimentation once they leave the mother cloud.
The sedimentation velocity vsed of a particle can then be expressed as a function of altitude z alone. This stationary solution conserves the particle number flux jp (i.e. the sedimentation velocity, particle number density and particle number
flux are functions of the altitude but do not explicitly depend
on time):
jp (z) = n(z) · vsed (z) = const .
(1)
Since vsed is roughly proportional to the square of the particle radius r (Müller and Peter, 1992), the particle acceleration due to growth alone, i.e. ignoring gas phase depletion, is
able to significantly reduce the particle number density. For
a dense mother cloud with n = 1 cm−3 an increase in radius from 1 µm (the approximate NAT particle radius in the
mother cloud in thermodynamic equilibrium) to 10 µm leads
to a reduction of the particle number density by two orders
of magnitude.
The particle number flux will not remain constant when
HNO3 gas phase depletion is taken into account. The falling
NAT particles remove HNO3 from the gas phase, and subsequent particles (falling through depleted air) will grow more
slowly and hence accelerate less readily, leading to a decrease in the particle flux. We show below that this effect
controls the particle flux in the vicinity of the cloud base,
but becomes less important with increasing distance from the
mother cloud, where particles fall rapidly and therefore denitrify less.
Atmos. Chem. Phys., 2, 93–98, 2002
Thus, there are two particle flux regimes: in the vicinity of
the cloud base, particle number flux is reduced by the HNO3
depletion by the sedimenting particles, here termed flux reduction layer (FRL). In contrast, sufficiently far below the
mother cloud the flux is approximately conserved (Fig. 1).
3
Description of the microphysical model
We use a 1-D microphysical model to study the physical processes taking place at the base of a mother cloud. The gas
phase is modeled on an irregularly spaced Eulerian grid with
8800 points. Centered at the cloud base, 8000 points are used
to model this important region with a vertical resolution of
1z = 1 cm. Elsewhere the vertical resolution is 10 m, covering a column from 15 km to 23 km altitude.
The NAT particles are modelled as individual particles,
storing particle positions and radii. About 50 000 particles
were required to obtain a statistically sufficient number of
particles at all altitude levels. The NAT particle size distribution in the mother cloud may be freely prescribed and is
chosen to be monodisperse for the base line calculation, with
the radius determined from the particle number density in
the mother cloud and the available HNO3 in thermodynamic
equilibrium. For each timestep (1t = 30 s) HNO3 partitioning between the gaseous and condensed phases is calculated from the kinetic growth/evaporation equations for the
NAT particles and by assuming equilibrium between the supercooled ternary solution (STS) droplets and the gas phase.
The HNO3 vapour pressure of NAT is calculated according to
Hanson and Mauersberger (1988), the partitioning into STS
according to Carslaw et al. (1995). Particle sedimentation
velocities are calculated including the Stokes and slip-flow
regimes (Müller and Peter, 1992). The shape of the particles undergoing growth/evaporation and sedimentation may
be prescribed and is chosen to be spherical in the base line
case.
The model was initialized with a constant H2 O volume
mixing ratio (VMR) of 5 ppmv and a constant total HNO3
VMR of 8 ppbv (typical for SOLVE/THESEO-2000 midwinter conditions). The time-independent temperature profile is chosen such that initially SNAT = 10 in the entire
column. This corresponds to a temperature of ≈ 3 K below TNAT and a negligible HNO3 partitioning into STS (less
than 1% for 0.1 ppbv H2 SO4 ). In the mother cloud, NAT
particles are then allowed to reduce the saturation ratio to
SNAT = 1. These idealized conditions have been chosen to
study the mechanism without effects caused by complex gas
phase and temperature profiles.
4
Results
Model calculations have been performed for a wide range of
cloud and gas phase parameters. Figure 2 shows the detailed
results for a monodisperse mother cloud with n = 0.1 cm−3
www.atmos-chem-phys.org/acp/2/93/
SNAT
20
18
(a)
mean radius [um]
16
22
20
18
16
(b)
n [cm-3]
22
20
18
16
(c)
jp [cm-2s-1 ]
22
20
18
16
(d)
22
20
18
16
0
11.0
8.8
6.6
4.4
2.2
0.0
12
(e)
20
40
60
time [h]
80
100
9
6
3
0
100
10-1
10-2
10-3
10-4
10-5
10-1
10-2
10-3
10-4
9.00
2.65
0.78
0.23
0.07
0.02
120
Fig. 2. 1-D model results for base line case as described in text. (a)
Saturation ratio SNAT (z, t) with SNAT = 1 in the mother cloud and
> 1 below. (b) – (e) Resulting radius r(z, t), number density n(z, t)
particle flux jp (z, t) and HNO3 mass flux jHNO3 (z, t). The minimum in the HNO3 flux (panel e) just below the mother cloud base
is a direct consequence of the strong particle number flux reduction
in this region (the Flux Reduction Layer). The total HNO3 is shown
in Fig. 4a.
(typical for type 1a-enh) and standard parameters mentioned
above.
The flux reduction layer (FRL), due to strong HNO3 depletion below the cloud base, causes an impressive reduction
in both particle number density (c) and flux (d) by 2 orders
of magnitude. Panel (e) shows the HNO3 mass flux. A flux
of 1 ppb × km/day corresponds to 1 ppb HNO3 being transported downward by 1 km within one day. The HNO3 mass
flux due to NAT-rocks reaches up to 9 ppb × km/day, while
it is 0.8 ppb × km/day within the mother cloud and remains
limited to the corresponding small altitude range.
A quantification of the effect of gas phase depletion,
caused by the sedimenting particles, on particle number density is given in Fig. 3. Particle number density profiles for the
base line case, a more dense (n = 1 cm−3 , all other parameters as in base line case) and a less dense (n = 0.01 cm−3 , all
other parameters as in base line case) mother cloud are compared to their corresponding stationary solution. Three conclusions follow from this comparison: (1) The decrease of
www.atmos-chem-phys.org/acp/2/93/
95
0.5
relative altitude [km]
22
jHNO3 [ppb.km/day]
altitude [km]
altitude [km]
altitude [km]
altitude [km]
altitude [km]
Fueglistaler et al.: NAT-rock formation by mother clouds
0.0
n [cm-3]
Mother
Cloud
n120 / nss
FRL
-0.5
-1.0
-1.5
10-4
(a)
-3
10
10
-2
10
-1
(b)
1 10
-2
10
-1
1
Fig. 3. (a) Vertical profiles of particle number density without gas
phase depletion (stationary solution, dashed lines) and with gas
phase depletion (full model, solid lines). All calculations use the
same parameters as the baseline case shown in Fig. 2, except for the
particle number density in the mother cloud (red: n = 1cm−3 ,
equil
equil
rNAT ≈ 0.6 µm; green: n = 10−1 cm−3 , rNAT ≈ 1.25 µm; blue:
equil
n = 10−2 cm−3 , rNAT ≈ 2.7 µm). The model results show the
number density profile after 5 days (120 h). The stationary calculations use the same initial conditions as the corresponding model
calculations but neglect gas phase depletion. (b) The number density of the model calculations after 5 days (n120 ) divided by the
number density of the corresponding stationary solution (nss ). This
ratio allows a quantification of the effect of the gas phase depletion
on particle number density reduction. The effect is most prominent
within a thin layer below the mother cloud, the flux reduction layer
(FRL).
particle number density due to gas phase depletion and due to
particle acceleration are of the same order of magnitude; (2)
The effect of gas phase depletion on particle number density
reduction is most prominent in a relatively thin layer just below the mother cloud, the flux reduction layer (FRL); (3) The
combination of particle acceleration and gas phase depletion
leads to particle number densities around 10−4 cm−3 a few
kilometers below the mother cloud, independently of the particle number density in the mother cloud. Hence, the suggested mother cloud/NAT-rock mechanism produces the observed NAT-rock particle number densities, n ≈ 10−4 cm−3 ,
from the whole range of mother cloud particle number densities.
The resulting total HNO3 VMR (gas plus condensed
phase) of the base line case is shown in panel (a) of Fig. 4,
allowing a quantification of denitrification. The most severe
denitrification is found in the FRL, where it reaches up to
75%. After 5 days, a vertical layer of about 2 km is denitrified by more than 50%. Conversely, more than 4 km below the mother cloud renitrification would result if all particles were to evaporate at this time. Each additional day with
>
SNAT ∼
1 increases the denitrification significantly.
Figure 4 compares the total HNO3 VMR of the base line
case (a) with two other relevant cases. Panel (b) refers to
Atmos. Chem. Phys., 2, 93–98, 2002
Fueglistaler et al.: NAT-rock formation by mother clouds
R
Table 1. Denitrification strength jHNO3 (z, t)dz
for t = 3 days
R
normalized to base line case (Fig. 2) with jHNO3 (z, t)dz =
14.6 km2 ppbv/day
22
20
18
16
12
(a)
total HNO3 [ppbv]
altitude [km] altitude [km] altitude [km]
96
22
20
18
16
(b)
22
20
10
0
6
4
2
0
(c)
20
40
60
80
time [h]
100
a less dense mother cloud (n = 10−2 cm−3 ). In this case,
the FRL does not develop strongly, but the flux conservation regime suffices to reduce number densities to about
10−4 cm−3 (see also Fig. 3), yielding a total HNO3 very similar to the base line case. Conversely, increasing the number
density within the mother cloud (n = 1 cm−3 ) strengthens
the role of the FRL (see also Fig. 3), again leaving the vertical redistribution of HNO3 at lower altitudes unchanged (not
shown). Panel (c) shows the effect of supercooled ternary
solution droplets (STS) on denitrification. In contrast to panels (a) and (b), here temperatures were chosen such that half
of the total HNO3 is taken up by STS, lowering the HNO3
VMR to initially 4 pbbv below the cloud. This leads to approximately halving the sedimentation distance of the NAT
particles below the mother cloud and a corresponding slowing of the denitrification process.
Model limitations and sensitivity tests
Various effects may alter the idealized computations shown
above, such as non-monodisperse size distributions, particle
shape, gas phase and eddy diffusion, and dynamical effects,
e.g. particle dispersion caused by wind shear. A measure of
the
R denitrification strength is the integrated HNO3 mass flux
dzjHNO3 (z, t). Table 1 compares various sensitivity runs in
terms of this quantity normalized to the base line result.
Atmos. Chem. Phys., 2, 93–98, 2002
base line case
aspheric particles (aspect ratio 1:3)
lognormal size dist. (σ = 1.4)
without gas diffusion
mother cloud with n =0.01 cm−3
mother cloud with n =1 cm−3
STS below mother cloud
1
1.03
1.03
0.99
1.37
0.91
0.73
120
Fig. 4. Total HNO3 (sum of gas phase and particulate). (a) Base
line case as in Fig. 2. (b) Mother cloud with n = 0.01 cm−3 , all
other parameters as in (a). Sedimentation begins earlier, but denitrification is less pronounced than in (a). (c) Total HNO3 for initially
SNAT =65 in entire column, which reduces to SNAT ≈ 30 due to
HNO3 uptake by STS aerosol, all other parameters as in (a). The
HNO3 -uptake of the STS aerosol delays sedimentation compared to
(a).
5
Norm. denitrification
strength
8
18
16
Scenario
Vertical thickness the of mother cloud. All calculations
assume an infinitely thick mother cloud to demonstrate the
basic properties of the sedimenting particles. A finite thickness limits the time particles can sediment out of the mother
cloud (which then eventually ceases to exist) but does not
affect the particle flux, number density or radius of the sedimenting particles. To allow ongoing sedimentation out of
>
the mother cloud for 5 or more days, a thickness of ∼
12 m,
>
>
68
m,
and
440
m
is
required
for
a
mother
cloud
with
∼
∼
n = 1 cm−3 , n = 0.1 cm−3 , and n = 0.01 cm−3 , respectively.
Effect of particle size distribution. A noteworthy aspect
is the insensitivity of denitrification to the initial size distribution. Lognormal and monodisperse distributions yield similar results as the particle number density reduction is dominated by the flux reduction/flux conservation scheme discussed above and not by preferrential sedimentation of initially larger particles. However, a wider distribution of particle sizes in the mother cloud yields also a wider distribution
of particle sizes in the sedimenting particle ensemble.
Particle shape. The asphericity of NAT particles affects
their sedimentation velocity and growth time. The sedimentation velocity of spherical particles is about 25% higher than
of aspherical particles with an aspect ratio of 1:3, which
serves as a case of extreme asymmetry (Müller and Peter,
1992). In addition, this small difference is partly compensated by more rapid growth of 5–10% of the aspherical particles.
Gas phase and eddy diffusion. Implementation of gas
phase diffusion in the model leads to an initially increased
HNO3 supply for particles above the cloud base, but changes
the results in Figs. 2–4 negligibly. The same holds true
for stronger eddy diffusion, although it leads to a more
pronounced transport of HNO3 into the mother cloud and
smoothing of the entire resulting HNO3 profile.
Dynamical effects. A microphysical column model canwww.atmos-chem-phys.org/acp/2/93/
Fueglistaler et al.: NAT-rock formation by mother clouds
not reflect the 3-D wind and temperature fields. Wind shear
leads to a distortion of the sedimenting particle ensemble,
and we may no expect to observe large NAT-particles directly
below type 1a/1a-enh PSCs. Furthermore, during mother
cloud formation, e.g. in a mountain lee wave event involving ice particles (Carslaw et al., 1998; Tsias et al., 1999;
Voigt et al., 2000), mesoscale variations in NAT particle
number density may initially obscure signs of sedimentation,
which become apparent only after about one day. In addition,
wind shear causes particles to sediment through different airmasses, which increases the volume of air denitrified by the
sedimenting particles (Dhaniyala et al., 2002).
6
Conclusions
This model study shows that type 1a and type 1a-enh PSCs
with n = 0.01 – 1.0 cm−3 can be a source of NAT-rocks,
which efficiently denitrify the polar vortex. Sensitivity studies show that the basic properties of the mother cloud/NATrock mechanism are surprisingly robust against changes
in the particle number density, size distribution and shape
within the mother cloud, as well as to gas phase or eddy
diffusion effects. Large scale transport and wind shear may
lead to geographic distortions of the sedimenting NAT-rock
population, but neither to enhanced nor reduced denitrification as long as the air remains supersaturated with respect
to NAT and mixing processes are not dominant. The resulting NAT-rock number densities and HNO3 vertical flux
agree well with in situ measurements. For 20 January, Fahey et al. (2001) estimate the particle number concentration
for the larger mode to be 2.3 × 10−4 cm−3 with a mode radius of 7.25 µm and a HNO3 flux of 2.6 ppbv × km / day.
Our model runs in Figs. 2 and 3 show particle number densities to range from 1 × 10−3 cm−3 about 2 km below the
mother cloud to less than 1 × 10−4 cm−3 at lower altitudes.
The modelled HNO3 flux a few kilometers below the mother
cloud ranges from 1 to 5 ppb × km/day, with a maximum of
9 ppb × km/day close to the leading edge of the sedimenting
NAT-rocks. The model indicates that severe denitrification
occurs only if the NAT particles sediment in ambient air with
temperatures below the NAT existence temperature for several days. Even in a very cold Arctic winter like the winter
1999/2000 (Manney and Sabutis, 2001), this requirement reduces the number of type 1a/1a-enh clouds which are suited
for the development of NAT-rocks.
Acknowledgements. We are grateful to S. Dhaniyala, K. A. McKinney, P. Wennberg, R. S. Gao and D. W. Fahey for fruitful and critical discussions. SF has been supported through
the EC-project THESEO-2000/EuroSOLVE (under contract BBW
99.0218-2, EVK2-CT-1999-00047) and through an ETHZ-internal
research project.
www.atmos-chem-phys.org/acp/2/93/
97
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